本研究是針對里歐諾夫黏彈性流體在單一切變流場下做數值解析以便了解其慣性項與對流項在高低速流場的影響效應。由於黏彈流體流動的模擬在數值技巧上有高度的複雜性尤其在高威森伯數的流場因此本研究結果對於里歐諾夫黏彈流體應用於其它複雜流場的模擬有相當大的助益。本文對於穩態、暫態以及全項的里歐諾夫方程式分別應用直接積分、有限差分法及有限元素法來求解。我們發現即使在高速(24cm/sec)的切變流場下，對流項與慣性項對於流動應力並不產生很大的影響。因此對於大多數熔態高分子流體加工條件而言，使用里歐諾夫模式作分析時，對流項及暫態項可以忽略不計。Numerical analysis of the Leonov viscolastic fluid in a unidirectional shear flow field has been performed in order to study the contributions of the accelation term and the convection term under high and low shear flow velocities. This study is of significant importance for the application of the Leonov model to the simulation of other complex flows because of the extreme numerical diffculties encountered in the analysis of the viscoelastic fiuid flow. Direct integration, finite difference method and finite element method are applied to obtain the solutions of the full-term, the transient and the steady-state Leonov equations. It has been found that the convection term and the transient term of the Leonov equation do not contribute significantly to the flow stress up to a flow velocity of 24 cm/sec which can be considered as a very high flow velocity for most most polymer-melt process conditions. However, when the full expression of the Leonov equation is used, the flow stresses will become fully developed without showing significanl overshoot phenomenon.